It's just like voting to close--five votes to close with a majority1 of migration votes will just migrate it over. There is no queue on destination site's side (though I would like oneI would like one), the whole process occurs on MO itself. If the folks at MSE close or delete it (except if it is marked as a duplicate), then the migration is "rejected", and the post is sent back to MO.
If unsure, you can always flag for moderator attention. Mods have a private chatroom called the Teacher's Lounge where they can discuss with other mods. It has a built in ping for summoning all mods of another site. However, the general policy is to simply migrate the post without asking (if the destination site doesn't like it, they can easily reject the migration). Teacher's Lounge pings are useful for edge cases when you'd like to learn about the site's scope by example.
FYI: "on hold" is functionally the exact same as "closed", jut nicer. The wording changes from "on hold" to "closed" in five days.
1. Not entirely sure if it needs a majority or all 5